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THE LOGIC OF QUANTIFIED STATEMENTS

“∀ real numbers x, if x is an integer then x is rational” “∀ integers x, x is rational” Both have informal translations “All integers are rational.” In fact, a statement can always be rewritten as by narrowing U to be domain D, where D is the truth set of P(x) (consisting of all values of variable x that make P(x) true).

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